When Speaker John Boehner (R-Ohio) was huddling this spring with top Democrats during the 2011 budget battle, House GOP aides were quietly engaged in a furious backroom effort to draft bills to ensure a shutdown of the federal government never happened.

But as high-profile talks over raising the U.S. debt limit reach a critical stage, there isn’t any escape hatch this time, at least not yet.

The House GOP leadership isn’t drafting alternative bills to boost the debt ceiling, and they’ve ruled out any short-term agreement to forestall a default by the U.S. government on its $14.4 trillion debt, an option that one House Republican lawmaker said could not muster more than 100 GOP votes.

With 12 legislative days before the White House’s deadline for a deal — and three weeks before Treasury’s Aug. 2 default date — House Republicans are counting on someone they haven’t had much faith in in the past: President Barack Obama.

“We’re putting stock in the president realizing he has to come up with a solution,” said Rep. Peter Roskam (R-Ill.), the chief deputy whip, who served with the president in the Illinois statehouse. “We’re waiting.”

Yet holding out for an overall agreement with Obama is a risky gambit, in part because the White House said Wednesday that it plans to push for an even bigger deal than House leaders envision, and one that could be hard to sell to Boehner’s restless rank and file.

GOP leaders are marching into the White House to meet with Obama and their Democratic counterparts on Thursday morning armed with blueprints devised during deficit talks on Capitol Hill, hoping to come to a final agreement with a president they have accused of slacking on the sidelines. Now, they have to reverse course and negotiate seriously with Obama on the biggest issue facing the 112th Congress.

In addition, Obama is pushing Republican leaders to accept revenue increases as part of an agreement, something they’re certain to reject, as they reiterated Wednesday that any final package must be revenue neutral.

White House officials said privately on Wednesday that Obama would push lawmakers to go for even bigger spending cuts than he had originally supported, as much as $4 trillion over a 10- to 12-year period. This comes from a recognition that Obama must push the next debt vote past the 2012 elections, and that to do so, he needs to take a more dramatic approach to spending cuts.

Inside the Capitol, where Boehner, Majority Leader Eric Cantor (R-Va.) and Senate Minority Leader Mitch McConnell (R-Ky.) must not only legislate but keep together groups of lawmakers loath to raise the nation’s debt cap, the road map to an agreement is incredibly complicated, especially among Republicans.

McConnell and Boehner — but especially the speaker — can only back a proposal that does not alienate their rebellious, tea-party-inspired freshmen. Any deal has to be a significant change in government spending patterns, now and in the future, big enough to convince junior lawmakers and the conservative base back home that GOP leaders are serious about ending the recent flood of federal red ink.

“It’s harder to get a majority of the [freshman] class on board for something that isn’t revolutionary,” said Rep. Tim Scott (R-S.C.), a freshman who is a member of leadership.

Boehner also has to watch his own flanks. He cannot, and will not, support a deal with Obama that isn’t backed by Cantor and House Majority Whip Kevin McCarthy (R-Calif.).

“If there was [an agreement] that got 75 Republicans and 150 Democrats, he’d have huge problems,” one GOP leadership aide said of Boehner. “He’s not going to do that.”

Boeher met with Cantor and other House GOP leaders on Wednesday afternoon, and he is scheduled to address the entire Republican Conference on Thursday morning, just hours before he heads to the White House.

And the reaction from Wall Street and the nation’s financial markets are factors that are of increasing concern to House lawmakers. GOP insiders say that any sudden drop in the Dow Jones Industrial Average, or signs from the bond market that there are concerns about official Washington’s wrestling over the debt cap, is likely to put increased pressure on lawmakers to move swiftly. One prominent House Republican said “Wall Street will send a clear message,” which could spur lawmakers into action.

Dan Clifton, a partner at Strategas, which monitors Washington for prominent hedge funds and New York firms, said the debate over the debt ceiling is the current obsession of financial players.

“Everybody is watching,” Clifton said in an interview Wednesday. Clifton said there’s a growing fear that Congress will be forced to agree on a short-term agreement, which would send a message to Wall Street that Washington won’t be able to get a deal done.

Then there are the mechanical hurdles. Once an agreement is reached, legislation must be drafted and scored by the Congressional Budget Office. Republicans then turn to the heady task of selling it to a House Republican Conference that is skeptical of any deal its leaders reach.

“This is a tough vote,” Cantor acknowledged Wednesday. “But in exchange for the vote what it is that our speaker has set as a goal is something really important. If we can accomplish this and begin at a $2.4 trillion cut as a down payment toward actually changing the way this place works, that’s the goal here. But yes, there’s going to be a lot of questions. A lot of members feel the same way I do, we weren’t elected to go and increase the credit limit.”

But there remain strong doubts among House Republicans, even in GOP leadership ranks, that Obama and Treasury Secretary Timothy Geithner are being candid about the impact of a U.S. debt default.

“Default of sovereign debt is a red herring. It’s not gonna happen,” House Republican Conference Chairman Jeb Hensarling of Texas said after exiting a leadership meeting Wednesday. “We’ve got enough money to pay bondholders, Medicare, Social Security, troops in the field. Frankly, as we all know, it gets challenging after that, but a [government collapse] doesn’t happen overnight. As you well know, debt can be rolled over. It’s not analogous to a government shutdown.”

House Democrats are also beginning to play an increasingly prominent role in the debt debate. While Senate Majority Leader Harry Reid (D-Nev.) and Obama have said they are open to cuts to Medicare, the popular seniors health program, House Minority Leader Nancy Pelosi (D-Calif.) will not back any agreement that makes structural changes to the program, including cuts in benefits. Pelosi and Democratic strategists know they cannot win the House back next year without being able to attack Republicans on Medicare cuts, so they will not back any agreement that deprives them of the issue.

House Minority Whip Steny Hoyer (D-Md.) also said Wednesday that “revenues need to be a significant part of” a debt deal but declined to offer specific tax increases he wanted to see in the final package.

Hoyer, who said he would provide Boehner with a significant number of Democratic votes for a deal that is to the minority’s liking, said the next few weeks will be important for defining lawmakers.

“I believe in this next 30 days, we’re going to see who are sunshine patriots and summer soldiers who are interested more in politics than responsibility, who are focused on the next election, not the next generation,” Hoyer told reporters Wednesday.